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. 2009 Jul 10;5(7):e1000434. doi: 10.1371/journal.pcbi.1000434

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Rafelski et al.

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.

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A) The bacterium is spatially discretized into 0.1 µm long mesh elements along the long-axis (the x-direction). In each of the mesh elements, two state variables and –the number of barbed-ends and the f-actin density, respectively– determine the element contribution to propulsion force and drag coefficient. B) Equations for , for example, are derived from conservation of barbed ends at a single mesh element: , where is the nucleation of new barbed-ends (i.e. a new mother filament), is the autocatalytic creation of barbed-ends from existing barbed-ends (i.e. branching), and is the velocity of the bacterium. Only elements on the hemispherical cap significantly contribute to propulsion force, while f-actin along the side of the bacterium contributes to the drag force. The ratio of force to drag determines the instantaneous velocity . A similar element diagram can be drawn for , though without any autocatalytic term. C) Steady state speeds for different ActA distributions. A constant drag on the bacterium led to faster normals than ultrapolars. Incorporation of a linear filament-dependent restraining mechanism, representing either (or both) filament-surface tethers or fluid coupling led to faster ultrapolars than normals, as in our experimental observations. A cooperative filament-dependent restraining mechanism (representing kinetic friction, for example) similarly led to faster ultrapolars (data not shown).

Inline graphic — A) The bacterium is spatially discretized into 0.1 µm long mesh elements along the long-axis (the x-direction). In each of the mesh elements, two state variables and –the number of barbed-ends and the f-actin density, respectively– determine the element contribution to propulsion force and drag coefficient. B) Equations for , for example, are derived from conservation of barbed ends at a single mesh element: , where is the nucleation of new barbed-ends (i.e. a new mother filament), is the autocatalytic creation of barbed-ends from existing barbed-ends (i.e. branching), and is the velocity of the bacterium. Only elements on the hemispherical cap significantly contribute to propulsion force, while f-actin along the side of the bacterium contributes to the drag force. The ratio of force to drag determines the instantaneous velocity . A similar element diagram can be drawn for , though without any autocatalytic term. C) Steady state speeds for different ActA distributions. A constant drag on the bacterium led to faster normals than ultrapolars. Incorporation of a linear filament-dependent restraining mechanism, representing either (or both) filament-surface tethers or fluid coupling led to faster ultrapolars than normals, as in our experimental observations. A cooperative filament-dependent restraining mechanism (representing kinetic friction, for example) similarly led to faster ultrapolars (data not shown).